M A R Y E T B O Y L E , P H . D .D E P A R T M E N T O F C O G N I T I V E S C I E N C E

U C S D

The Neuronal Membrane at Rest

Understanding the ionic basis for the resting potential

Describe the concept of electrochemical equilibrium and relate this concept to the resting membrane potential of

neurons.

Explain why the permeability of the neuronal plasma membrane at rest to K+ and the concentrationgradient of this ion across the neuronal plasma membrane account

for the resting membrane potential of neurons.

Use the NERNST EQUATION to predict the resting membrane potential of neurons given knowledge of the

concentration gradients of permeant ions..Learning

objectives

Overview - Neurons generate electrical signals

Problem: neurons are poor at conducting electricity.

Solution: evolved mechanism to overcome limitations.

How: electrical signals are based on the flow of ions across the plasma membrane.

Action potential in the nervous system

Collect distribute integrate

Consider the following experimental setup:

record

stimulate

Microelectrode to measure membrane potential

Microelectrode to inject current

neuron

The experiment:

record

stimulate

Comparison of electrical problems…

Copper wire

Electrical charge is carried by free electrons

Well insulated‐plastic coating; air

Great conductor

Cytosol in Axon

Electrical charge is carried by ions.

Not perfectly insulated; salty extracellular fluid will

conduct electricity

Less than perfect conductive medium!

Two basic concepts critical to understanding neuronal signaling…

Charge

Ions are needed to carry the electrical charge

Concentration gradient is a means to store energy

FlowPermeability mechanism to redistribute ions across the

membrane

Ion flow regulation and management

Essential Resting Membrane Potential Properties:

Salty fluids on either side of the membrane

The membrane

Proteins that span the membrane

Distinguishing between the role of channels and pumpsin establishing the concentration gradient.

Two permeability mechanisms:

PUMPS are used to create ion gradients – actively moves ions

against gradient

CHANNELS allow ions to diffuse down concentration gradient

Water Key ingredient in intracellular and extracellular fluid Key feature – water is a polar solvent – which means thatother polar molecules tend to dissolve in water.

Cytosolic and Extracellular Fluid

Net negative charge

Net positive charge

Why does NaCl crystal dissolve in water?

NaCl dissolves in water because the polar water molecules have a stronger attraction for the electrically charged sodium and chloride ions than the ions do for one another.

Cations: ions with a net positive chargeAnions: ions with a net negative charge

Ions: Atoms or molecules with a net electrical charge

cations • Na+, K+, Ca++

anions • Cl-

Major charge carriers in the neuron:

Hydrophilic v. Hydrophobic

‐philic

Dissolve in water

Uneven electrical charge

NaCl

‐phobic

Do NOT dissolve in water

Shared electrons are distributed evenly

lipids

Phospholipid bilayer: the cell membrane

• Neuronal membrane is a sheet of phospholipids two molecules thick.

• Hydrophilic heads face the outside and inner watery environments

• Hydrophobic tails face each other.

Polar “head” containing phosphate

Non-polar ‘tail” containing hydrocarbon

H3N+

H

COO-

R

C

Central alpha carbonAmino group

Hydrogen atom

Carboxyl group

Variable R group

Recall, the basic Structure of an amino acid

Other amino acids

Strongly hydrophilicR groups

Strongly hydrophobic

R groups

Peptide bonds and polypeptides

Four levels of protein structure

primary structure

secondary structure

tertiary structure

quarternary structure

Thinking about channels

Nonpolar R groupshydrophobic

Polar R groups(Hydrophilic)

Diameter of pore

R-Groups lining

the pore

Gating Ion pumps

Ion specificity is determined by:

Ion channels can be opened and

closed by changes in the

local micro-environment of the membrane.

The Movement of Ions- Factor #1: Diffusion

Dissolved ions distribute evenly Ions flow down concentration gradient when:

Channels permeable to specific ionsConcentration gradient across the membrane

Impermeable membrane Na+ and Cl- channels Equal distribution of ions

A channel across a membrane is like a bridge across a river.

A gated channel is a like a

drawbridge.

The Movements of Ions- Factor #2: Electricity

Cl-Na+

Movement of ions are influenced by electrical fields.

Recall: opposite charges attract and like charges repel.

Place wires from two terminals of a battery in a solution containing

dissolved NACl.

The movement of electrical charge is called electrical current (I) and measured in units called

amperes (amps).

By convention, current flows from + to –

Two important factors determine how much current

will flow:

Electrical potential&

Electrical conductance

Current flow

Electrical potential - voltage

Electrical potential is the force exerted on a charged particle

It reflects the difference in electric potential per unit charge between the

anode and the cathode

More current will flow as this difference is increased.

Voltage is represented by the symbol V and is

measured in volts.

The difference in electrical potential

between the terminals of a car battery is 12V.

Electrical conductance (g)

Is the relative ability of an electrical charge to migrate from one point to another.

It is represented by the symbol g and measured in units called Siemens (S).

Conductance depends on the number of

particles available to carry electrical charge‐

and the ease with which these particles can travel through

space

Electrical resistance (R) relative inability of the charge to migrate.

Resistance is the inverse of

conductance.R =

R = Resistance is

represented by the symbol R and is measured in units called ohms (Ω)

Ohm’s Law: V=IR

RIV

How would you express Ohm’s law using conductance (g) instead of resistance?

_____________

Express Ohm’s law as: I = _______

How much current (I) will flow if:How much current (I) will flow if:

Recall: Ohm’s lawRecall: Ohm’s law1. g = 0 and V=100?

2. V = 0 and g=30?

Current (I) =conductance (g) * potential difference (V)

Example 1:

What would happen if NaCl were dissolved

in equal concentrations on

either side of a phospholipid bilayer?

Na+Cl- Na+Cl-

Example 1:

What would happen if NaCl were dissolved

in equal concentrations on

either side of a phospholipid bilayer?

Na+Cl-

Na+Cl-Na+Cl-

Na+Cl-

Example 1:

What would happen if NaCl were dissolved

in equal concentrations on

either side of a phospholipid bilayer?

Na+

Cl-

Na+

Cl-

There will be a large potential difference across

the membrane.

No current will flow –because there are no channels to allow the migration of Na+ and Cl‐across the membrane.

Example 2:

Now, what would happen ??

Na+

Cl-

Na+

Cl-Current

flow

To drive ions across the membrane electrically:

(1) the membrane possesses channels permeable to that ion and

(2) there is an electrical potential difference across the membrane.

Current flow

The Ionic Basis of The Resting Membrane Potential

A voltmeter measures the difference in electrical potential between the tip of a microelectrode inside the cell and a wire placed in the extracellular fluid.

glass microelectrode

intracellular

ground

amplifierwire

Extracellular bath

A- Any negative charged ion.

[20 inside] : [1 outside]Large concentration gradient exists between the inside of the cell and the outside.

No channel proteins.

Vm = 0 mVVm = ??? mV

No net movement of ions when separated by a phospholipid

membrane – and the K+:A- ratio remained the same.

[K+:A-=1] : [K+:A-=1 ]

Model System:

inside outside

voltmeter

1mM KCl 1mM KCl

• Chamber with two compartments• Add channels

• Only permeable to K+• Each chamber is filled with 1mM KCl• K is free to move from one chamber to

the other• No next flux of K• Voltage recorded by voltmeter is: 0mV

What would happen if :• Added 10mM KCl inside vs. 1mM KCl outside• Channels are only permeable to K+• K + is free to move from one chamber to the other

inside outside

10mM KCl 1mM KCl

inside outside

10mM KCl 1mM KCl

?mVInitial

conditions:

Vin‐out =

Electrochemical Equilibrium:

• The flux of K+ from the inside is EXACTLYbalanced by an opposing membrane potential

• For example, as K+ diffuses down its concentration gradient an electrical force builds up that is exactly equal and opposite to the strength of the chemical gradient.

inside outside

10mM KCl 1mM KCl

?mVVin‐out =

A- Any negative charged ion.

Selective permeability K+ can move between the inside and outside but A- cannot

ADD K+ channels

Initially, K+ ions would get out of the cell along the steep concentration gradient.

Vm = ??? mV

Eventually diffusion and electrostatic pressures are perfectly balanced and ….

A- Any negative charged ion.

Selective permeability K+ can move between the inside and outside but A- cannot

Diffusional and electrical forces are equal and opposite.

Net movement across the membrane ceases.

Vm = ??? mV

EQUILIBRIUM POTENTIALEion represents the ionic

equilibrium potential.

Eion = Vm mV

Equilibrium Potential(Eion)

No net movement of ions when separated by a phospholipid membrane

Equilibrium reached when K+channels inserted into the phospholipid bilayer

Electrical potential difference that exactly balances ionic concentration gradient

4 points of Equilibrium Potentials

Large changes in VmMinuscule changes in ionic concentrations

Net difference in electrical chargeInside and outside membrane surface

Rate of movement of ions across membrane –ionic driving forceProportional Vm – Eion

Concentration difference known for an ion:Equilibrium potential can be calculated

Distribution of Electrical Charge

The uneven charges inside and outside the neuron line up along the membrane because of electrostatic attraction across the very thin barrier.

Notice that the bulk of the cytosol and extracellular fluid is electrically neutral.

Steps to establishing Eion

Steps to establishing the equilibrium potential of Na+

The Nernst Equation

Calculates the exact value of the equilibrium potential for any permeant ion (mV) Takes into consideration:

R Gas constant z Valence of the permeant ion (electrical charge) T Temperature (absolute – degrees Kelvin) F Faraday constant (amount of electrical charge in a mole of a univalent ion [ion]o concentration of ion outside of the cell [ion]I concentration of ion inside of the cell

Eion = Ionic equilibrium potential

R = Gas constant

T = Absolute temperature

z = Charge of the ion

F = Faraday’s constant

log = Base 10 logarithm

[ion]o = Ionic concentration outside the cell

[ion]i = Ionic concentration inside the cell

EK = 61.54 mV log

ENa = 61.54 mV log

ECl = ‐61.54 mV log

ECa = 30.77 mV log

At body temperature (37°C), the Nernst

equation for the important ions, K+, Na+, Cl‐ and Ca++simplify to:

=

= ‐1.3

EK = 61.54 mV ‐1.3

= 80 mV

If

and

then

=

=

ENa = 61.54 mV

= mV

If extracellular sodium is 10x greater than the intracellular sodium:

andthe neuronal membrane is selectively permeable onlyto sodium ‐

What will the resting membrane potential be?

The Distribution of Ions Across The Membrane

K+ more concentrated on inside, Na+ and Ca2+ more concentrated outside

What is the Equilibrium Potential for an Ion?

An equilibrium potential for an

ion is -

the membrane

potential that results if a

membrane is selectively

permeable to that ion alone

The sodium-potassium pump

Enzyme ‐ breaks down ATP in the presence of internal Na Pump exchanges internal Na for external K

Calcium Pump

An enzyme that actively transports Ca++out of the cytosol.

Additional mechanisms decrease intracellular Ca++ to a

very low level (0.0002mM)

Intracellular calcium‐binding proteins and

organelles –mitochondria and ER that sequester Ca++

What would happen to Vm if the membrane were EQUALLY permeable to K+ and Na+?

Vm would equal some average of EK and ENa

What would happen to Vm if the membrane were 40x more permeable to K+ than to Na+?

Vm would be between EK and ENa but much closer to EK than Ena this approximates what happens in real neurons.

The resting membrane potential of -65mV approaches, but does not achieve, the potassium equilibrium potential of -80mV.

This difference arises because, although the membrane at rest is highly permeable to K, there is also a steady leak of Na into the cell.

Relative Ion Permeabilities of the Membrane at Rest

Recall, the Nernst equation is about Vm if a membrane is selectively permeable to that ion alone.

However, neurons are permeable to more than one type of ionMembrane permeability determines membrane potential

Goldman equationTakes into account permeability of membrane to different ions

Calculating the Vm using the Goldman Equation

K+ • [K]o=5mM• [K]i=100mM

Na+ • [Na]o=150mM• [Na]i=15mM

Permeability @ rest

•K+ is 40 x > Na+

Assumptions:

The Goldman Equation

is the membrane potential.and are the relative permeabilities to K and Na ions

Constants are the same as in the Nernst equation

If the resting membrane ion permeability is to K+

is 40 times greater than it is to Na+, then solving:

Vm = 61.54mV log

= 61.54mV log

= ‐65mV

NATURE REVIEWS | NEUROSCIENCE VOLUME 3 | FEBRUARY 2002

Choe, S (2002)

The four main classes of potassium channels. a | 2TM/P channels (which consist of two transmembrane (TM) helices with a P loop between them), exemplified by inwardly rectifying K+ channels and by bacterial K+ channels such as KcsA. b | 6TM/P channels, which are the predominant class among ligand‐gated and voltage‐gated K+ channels. c | 8TM/2P channels, which are hybrids of 6TM/P and 2TM/P, and were first found in yeast. d | 4TM/2P channels, which consist of two repeats of 2TM/P channels. 8TM/2P and 4TM/2P probably assemble as dimers to form a channel. 4TM/2P channels are far more common than was originally thought. These so called ‘leakage’ channels are targets of numerous anesthetics. S4 is marked with plus signs to indicate its role in voltage sensing in the voltage‐gated K+ channels.

Crystallographic structure of the bacterial KcsApotassium channel (PDB 1K4C).In this figure, only two of the four subunits of the tetramer are displayed for the sake of clarity. The protein is displayed as a green cartoon diagram. In addition backbone carbonyl groups and threonine side chain protein atoms (oxygen = red, carbon = green) are displayed. Finally potassium ions (occupying the S2 and S4 sites) and the oxygen atoms of water molecules (S1 and S3) are depicted as purple and red spheres respectively.

Choe, S (2002)

Resting Membrane Potential is Close to Ek

Resting membrane potential is close to EK because it is mostly permeable to K+

Membrane potential sensitive to extracellular K+

Increased extracellular K+ depolarizes membrane potential

A tenfold change in [K+]o from 5 to 50mM, causes a 48mV depolarization of the membrane.

Increasing extracellular K+ from 5mM to 50mM causes a 48mV depolarization

10x

∆ 48mV

Increasing extracellular K depolarizes the

neuron!

Increasing extracellular K depolarizes the

neuron!

Regulating the External K Concentration

Blood‐Brain barrier Limits the movement of potassium into the extracellular fluid.

Potassium spatial buffering Astrocytes have membrane potassium pumps and channels that concentrate K+ in their cytosol.

http://www.nytimes.com/2011/06/04/us/04kevorkian.html?pagewanted=all

Concepts to Remember

Activity of the sodium‐potassium pump Large K+ concentration gradient Electrical potential difference across the membrane Similar to a battery

Potassium channels Contribute to resting potential

Roles of ion pumps